Jo Boaler: How to Learn Math | Lex Fridman Podcast #226

1. 0:00 – 0:23

   Introduction

   1. LFLex Fridman0:00

      The following is a conversation with Jo Boaler, a mathematics educator at Stanford and co-founder of youcubed.org that seeks to inspire young minds with the beauty of mathematics. To support this podcast, please check out our sponsors in the description. This is the Lex Fridman podcast and here is my conversation with Jo Boaler.

2. 0:23 – 9:12

   What is beautiful about mathematics?

   1. LFLex Fridman0:23

      What to you is beautiful about mathematics?

   2. JBJo Boaler0:27

      I love a mathematics that some people don't even think of as mathematics (laughs) , which is beautiful, creative mathematics where we look at maths in different ways, we visualize it, we think about different solutions to problems. A lot of people think of maths as you have one method and one answer, and what I love about maths is the multiple different ways you can see things, different methods, different ways of seeing, different... in some cases, different solutions. So that is what is beautiful to me about mathematics, that you can see and solve it in many different ways. And also, the sad part that many people think that maths is just one answer and one method.

   3. LFLex Fridman1:13

      Mm-hmm. So to you the beautiful, the beauty emerges when you have a problem with a solution and you start adding other solutions, simpler solutions-

   4. JBJo Boaler1:22

      Mm-hmm.

   5. LFLex Fridman1:23

      ... uh, weirder solutions, more interesting-

   6. JBJo Boaler1:25

      Yeah.

   7. LFLex Fridman1:25

      ... some that are visual, some that are algebraic, geometry, all that kind of stuff.

   8. JBJo Boaler1:30

      Yeah. I mean, I, I always say that you can take any maths area and make it visual.

   9. LFLex Fridman1:35

      Mm-hmm.

   10. JBJo Boaler1:35

       And we say to teachers, "Give us your most dry, boring maths and we'll make it a visual, interesting, creative problem." And turns out you can do that with any area of maths. And I think we've given pe- it's been a great disservice to kids and others that it's always been numbers, lots and lots of numbers. Numbers can be great, but you can think about maths in other ways besides numbers.

   11. LFLex Fridman2:01

       Do you find that most people are better visual learners or is this just something that's complementary? The, uh, what, what's the kind of the full spectrum of students-

   12. JBJo Boaler2:11

       Mm-hmm.

   13. LFLex Fridman2:11

       ... and the way they like to explore math would you say?

   14. JBJo Boaler2:13

       I mean, there's definitely people who come into the classes I do who are more interested in visual thinking and like visual approaches, but it turns out, what the neuroscience is telling us, is that when we think about maths there are two visual pathways in the brain and we should all be thinking about it visually. Some approaches have been to say, "Well, you're a visual learner so we'll give you visuals," and, "You're not a visual learner." But actually if you think you're not a visual learner, it's probably more important that you have a visual approach so you can develop that part of your brain.

   15. LFLex Fridman2:51

       So you were saying that there's some kind of interconnected aspect to it, so the visual connects with the nonvisual?

   16. JBJo Boaler2:56

       Yeah. So this is what the neuroscience has shown us that when you work on a maths problem there are five different brain pathways and that the most high achieving people in the world are people who have more connections between these pathways.

   17. LFLex Fridman3:10

       Mm-hmm.

   18. JBJo Boaler3:10

       So if you see a maths problem with numbers but you also see it visually, that will cause a connection to happen in your brain between these pathways. And if you maybe write about it with words, that would cause another connection, or maybe you build it with something physical, that would cause a different connection. And what we want for kids is, we call it a multidimensional experience of maths, seeing it in different ways, experiencing it in different ways. That will cause that great connected brain.

   19. LFLex Fridman3:40

       Y- you know there's these stories of physicists doing the same. I find physicists are often better at building that part of their brain of, uh, using visualization-

   20. JBJo Boaler3:49

       Mm-hmm.

   21. LFLex Fridman3:49

       ... for intuition building 'cause you ultimately want to understand the like, the deepest secret underneath this problem and for that you have to s- intuit your way there.

   22. JBJo Boaler3:59

       Yeah.

   23. LFLex Fridman3:59

       And you, you mentioned offline that, um, one of the ways you might approach a problem is to try to tell a story about it.

   24. JBJo Boaler4:05

       Mm-hmm.

   25. LFLex Fridman4:05

       And some of it is like legend, but I'm sure it's not always 'cause, you know, you have Einstein, uh, thinking about a train, you know, and the speed-

   26. JBJo Boaler4:15

       Mm-hmm.

   27. LFLex Fridman4:15

       ... of light and, you know, that kind of intuition is useful.

   28. JBJo Boaler4:19

       Yeah.

   29. LFLex Fridman4:20

       You start to like imagine a physical world, like how does this idea manifest itself in the physical world? And then start playing in your mind with that physical world-

   30. JBJo Boaler4:28

       Mm-hmm. Mm-hmm.
3. 9:12 – 17:31

   How difficult should math really be?

   1. JBJo Boaler9:12

   2. LFLex Fridman9:12

      You say that, uh, there's something about, there's something valuable to learning when the thing that you're doing is challenging, is difficult. So a lot of people say, you know, math is hard or math is too hard or too hard for me. Do you think math should be easy or should it be hard?

   3. JBJo Boaler9:33

      I think it's great when things are challenging but there's something that that's really key to being able to deal with challenging maths and that is knowing (laughs) that you can do it. And I think the problem in education is a lot of people have got this idea that you're either born with a maths brain or you're not. So when they start to struggle, they think, "Oh, I don't have that maths brain." And then they will literally sort of switch off in their brain and things will go downhill from that point. So struggle becomes a lot easier and you're able to struggle if you don't have that idea, but you know that you, you can do it. You have to go through this struggle to get there but you're, you're able to do that. And so we're hampered in being able to struggle with these ideas we've been given about what we can do.

   4. LFLex Fridman10:25

      Can I ask a difficult question here?

   5. JBJo Boaler10:27

      Yeah. (laughs)

   6. LFLex Fridman10:27

      So there's kind of, um, I don't know what the right term is, but some people are, um, struggle with learning in different ways. Like their brain is constructed in different ways.

   7. JBJo Boaler10:41

      Mm-hmm.

   8. LFLex Fridman10:42

      And, um, how much should, as educators, should we make room for that? So how do you know the difference between this is hard-

   9. JBJo Boaler10:52

      Mm-hmm.

   10. LFLex Fridman10:52

       ... and I don't like doing hard things versus my brain is wired in a way where I need to learn in very different ways, I can't learn it this way?

   11. JBJo Boaler11:00

       Mm. Mm.

   12. LFLex Fridman11:00

       How do you find that line? How do you operate in that gray area?

   13. JBJo Boaler11:04

       Mm. So this is why being a teacher is so hard and people really don't appreciate how difficult teaching is when you're faced with, I don't know, 30 students (laughs) who think in different ways and, um, but this is also why I believe it's so important to have this multidimensional approach to maths. We've really offered it in one way which is, "Here's some numbers and a method, you follow me, do what I just did and then reproduce it." And so there are some kids who like doing that and they do well and a lot of kids who don't like doing it and don't do well. But when you open up maths and you give, you let kids experience it in different ways, maybe visually, with numbers, with words, what happens is kids, there are many more kids who can access it.

   14. LFLex Fridman11:52

       Mm-hmm.

   15. JBJo Boaler11:52

       So those different brain wirings you, you're talking about where some people are just more able to do something in a particular way, that's why we want to, that's one of the reasons we want to open it up so that there are different ways of accessing it, and then that's not really a, a problem.

   16. LFLex Fridman12:11

       So I, uh, grew up in the Soviet Union and, uh, fell in love with math early. I was forced into math early and fell in love.... through force.

   17. JBJo Boaler12:22

       That's good.

   18. LFLex Fridman12:23

       (laughs)

   19. JBJo Boaler12:23

       Well, good that you fell in love about the force.

   20. LFLex Fridman12:25

       Well, but there, uh, something we, we talked about a little bit is there is such, um, value for excellence. Uh, it's competitive and, and it's also everybody kind of looks up. The d- the definition of success is being, uh, in a particular class as, you know, being really good at it.

   21. JBJo Boaler12:46

       Mm-hmm. Mm-hmm.

   22. LFLex Fridman12:47

       Um, and like it's not improving, it's like being really good. I mean, we are much more like that with sports, for example. We're not... It's like it's understood, you know, you're going to star on the basketball team if, uh... You're gonna start on the basketball team if you're going to be better than-

   23. JBJo Boaler13:04

       Mm-hmm.

   24. LFLex Fridman13:04

       ... the other guys, the other girls on the team.

   25. JBJo Boaler13:06

       Mm-hmm.

   26. LFLex Fridman13:07

       Uh, so that coupled with the belief... This could be partially a communist belief, I don't know, but the belief that everybody is capable of being great. But if you're not great, that's your fault-

   27. JBJo Boaler13:21

       Mm-hmm.

   28. LFLex Fridman13:22

       (laughs) And you need to work harder and... I remember I had a sense that, um, probably delusional, but I could win a Nobel Prize. I didn't even know what that entails, um, but I thought, um, like, uh, my dad early on told me just offhand and it always stuck with me, that if you, if you can figure out how to build a time machine, how to travel back in time, it will probably give you a Nobel Prize. And I remember early in my life thinking, "I'm going to invent a time machine."

   29. JBJo Boaler13:52

       (laughs) That's-

   30. LFLex Fridman13:52

       And like, like the tools of mathematics were in service of that dream of winning the Nobel Prize. And there, i- it's silly, I didn't really think in those concrete terms, but I just thought I could be great, that feeling.
4. 17:31 – 28:52

   Students giving up on math

   1. LFLex Fridman17:31

      Is there, um... Could you comment on what age is like the most important when people quit math or give up on themselves or on math in general, and, uh, perhaps that age or something earlier is really i- uh, important moment for them-

   2. JBJo Boaler17:48

      Mm-hmm.

   3. LFLex Fridman17:48

      ... to discover, to be inspired to discover-

   4. JBJo Boaler17:49

      Yeah.

   5. LFLex Fridman17:49

      ... the magic of math?

   6. JBJo Boaler17:51

      I think a lot of kids start to give up on themselves and maths around, from about fifth grade, and then those middle school years are really important.

   7. LFLex Fridman18:01

      Wow.

   8. JBJo Boaler18:02

      And fifth grade can be pivotal for kids just because they're allowed to explore and think in good ways in the early grades of elementary school, but fifth grade teachers are often like, "Okay, we're gonna prepare you now for middle school and we're gonna give you grades and lots of tests," and that's when kids start to feel really badly about themselves. And so middle school years, we... Our camps are middle school students, we think of those years as really pivotal. Many kids in th- in those years are deciding, yes, I'm gonna keep going with STEM subjects-... "Oh, no, I'm not, that this isn't for me." So, I mean, all years are important and in all years you can kind of switch kids and get them on a different pathway, but I think those middle school years are really important.

   9. LFLex Fridman18:48

      So, what's the role of the teacher in this? So, one is the explanation of the subject, but do you think teachers should almost do like one-on-one, you know, "Little Johnny, I believe in you," kind of thing?

   10. JBJo Boaler19:01

       Yeah. (laughs)

   11. LFLex Fridman19:02

       Like that, that energy of like...

   12. JBJo Boaler19:03

       Turns out it's really important. There's, um, a study that was done, and it was actually done in high school English classrooms, where all kids wrote an essay for their teacher, and this was done as an experiment. Half of the kids got feedback from their teacher, diagnostic feedback, which is great. But for half of the kids it said an extra sentence at the bottom that the researchers had put on.

   13. LFLex Fridman19:25

       Mm-hmm.

   14. JBJo Boaler19:26

       And the kids who read that extra sentence did significantly better in English a whole year later. The only change was this one sentence.

   15. LFLex Fridman19:36

       What did the sentence say? (laughs)

   16. JBJo Boaler19:37

       So, what did the sentence say? The sentence said, "I'm giving you this feedback because I believe in you." And the kids who read that did better a year later.

   17. LFLex Fridman19:48

       Yeah.

   18. JBJo Boaler19:49

       So, when I share this with teachers, I say, you know, "I'm not suggesting you put on the bottom of all kids' work, 'I'm giving you this feedback because I believe in you.'" One of the teachers said to me, "We don't put it on a stamp?" I said, "No. Don't put it on a stamp. It's, um..." But your words are really important. And kids are sitting in classrooms all the time thinking, "What does my teacher think of me? Does my teacher think I can do this?" Um, so it turns out it is really important to be saying to kids, "I know you can do this." And those messages are not given enough by teachers.

   19. LFLex Fridman20:27

       And really believe it.

   20. JBJo Boaler20:29

       And believe it, yeah.

   21. LFLex Fridman20:29

       Yeah. It's like, uh-

   22. JBJo Boaler20:30

       You can't just say it, you have to believe it.

   23. LFLex Fridman20:32

       I, I, I sometimes, 'cause like... it's, it's such a funny dance 'cause I'm, I'm such a perfectionist that I'm, I'm extremely self-critical. And I have, when I have students come up to me and it's clear to me that they're not even close to good, and it's tempting for me to be like... uh, to sort of give up on them mentally.

   24. JBJo Boaler20:53

       Mm-hmm. Mm-hmm.

   25. LFLex Fridman20:54

       But the reality is, like if you look at many great people throughout history, they sucked at some point. (laughs)

   26. JBJo Boaler21:00

       Yeah, exactly.

   27. LFLex Fridman21:01

       And they... And, and some of the greatest took non-linear paths-

   28. JBJo Boaler21:04

       Yeah.

   29. LFLex Fridman21:04

       ... to where they sucked for long into li- into-

   30. JBJo Boaler21:07

       Mm-hmm.
5. 28:52 – 38:49

   Improving math education in schools

   1. JBJo Boaler28:52

   2. LFLex Fridman28:52

      Is there for a teacher, if we were to like systematize it, is there something teachers can do to do this more effectively? So you mentioned-

   3. JBJo Boaler29:02

      There is.

   4. LFLex Fridman29:02

      ... you mentioned the textbook.

   5. JBJo Boaler29:04

      Yeah.

   6. LFLex Fridman29:04

      So, so what, what are the additional things you can add on top of this whole old school traditional way of teaching-

   7. JBJo Boaler29:11

      Mm-hmm. Mm-hmm.

   8. LFLex Fridman29:12

      ... that can improve the, the process?

   9. JBJo Boaler29:14

      So I do think there's a way of teaching maths that changes everything for kids, uh, and teachers. So I'm one of five writers of a new framework for the state of California, a new math framework. It's coming out next year. And we are recommending through this maths framework that people teach in this way. It's called Teaching to Big Ideas.

   10. LFLex Fridman29:37

       Mm-hmm.

   11. JBJo Boaler29:38

       So, um, at the moment, people have standards that have been written and then textbooks have taken these standards and made not very good questions.

   12. LFLex Fridman29:48

       Mm-hmm.

   13. JBJo Boaler29:48

       And if you look at the standards, like I have some written down here, just reading the standards, it makes maths seem really boring and uninspiring.

   14. LFLex Fridman29:57

       What, what are, what are the kind of, can you give a few examples what-

   15. JBJo Boaler30:01

       So this is an, an interesting example. In third grade, there are three different standards about unit squares.

   16. LFLex Fridman30:08

       (laughs) Okay.

   17. JBJo Boaler30:11

       Um, so this is one of them. "A square with side length one unit called a unit square is said to have one square unit of area and can be used to measure area."

   18. LFLex Fridman30:20

       And that's something you're expected to learn.

   19. JBJo Boaler30:23

       That is something, that's, so that's a standard. The textbook authors say, "Oh, I'm gonna make a question about that," and they translate the standards into narrow questions.

   20. LFLex Fridman30:32

       And then you measure success by your ability to deliver on, o- on these standards.

   21. JBJo Boaler30:36

       Yes. Mm-hmm.So, the standards themselves, uh, I, I think of maths, and many people think of maths in this way, as a subject of like a few big ideas and really important connections between them. Um, so like in, you could think of it as like a network map of ideas and connections.

   22. LFLex Fridman30:52

       Mm-hmm.

   23. JBJo Boaler30:52

       And what standards do is they take that beautiful map and they chop it up like this into lots of little pieces and they deliver the pieces to schools and so teachers don't see the connections between ideas, nor do the kids. So anyway, this is a bit of a long way of saying that what we've done in this new initiative is we have set out maths as a set of big ideas.

   24. LFLex Fridman31:15

       Mm-hmm.

   25. JBJo Boaler31:16

       And connections between them. So this is um, grade three.

   26. LFLex Fridman31:20

       Mm-hmm.

   27. JBJo Boaler31:20

       So instead of there being 60 standards, we've said well you can pull these different standards to get in with each other and um, also value the ways these are connected.

   28. LFLex Fridman31:38

       And by the way, for people who are just listening, we're looking at a small number of uh, like big concepts within mathematics.

   29. JBJo Boaler31:45

       Mm-hmm.

   30. LFLex Fridman31:45

       Square tiles, measuring, fraction, shape and time, and then how they're interconnected.
6. 38:49 – 56:35

   Inspiring mathematical creativity

   1. LFLex Fridman38:49

      at those early few days when you just wanna capture them?

   2. JBJo Boaler38:53

      I do something... actually, there's a video of me doing this on our website, that I love when I first meet students. And this is what I do. I show them a picture. This is the picture I show them, and it's a picture of seven dots like this.

   3. LFLex Fridman39:11

      Mm-hmm. (paper rustles)

   4. JBJo Boaler39:13

      And I show it for just a few seconds, and I say to them, "I'd like you just tell me how many dots there are, but I don't want you to count them. I want you to group the dots." And I show it them and then I, I, I take it away before they've even had enough time to count them. And then I ask them, "So how did you see it?" And I go around the room and, amazingly enough, there's probably 18 different ways of seeing these seven dots.

   5. LFLex Fridman39:38

      (laughs) Mm-hmm.

   6. JBJo Boaler39:39

      And so, I ask people, "Tell me how, how you grouped it." And some people see it as like an outside hole with a center dot.

   7. LFLex Fridman39:45

      Mm-hmm.

   8. JBJo Boaler39:45

      Some people see like stripes-

   9. LFLex Fridman39:47

      Mm-hmm.

   10. JBJo Boaler39:48

       ... of lines. Some people see segments. And I collect them all and I put them on the board, and at the end I say, "Look at this. We are a class of 30 kids and we saw these seven dots in 18 different ways." There's actually a mathematical term for this. It's called groupitizing.

   11. LFLex Fridman40:03

       Mm-hmm. Groupitizing?

   12. JBJo Boaler40:04

       Yeah.

   13. LFLex Fridman40:05

       (laughs) I like it.

   14. JBJo Boaler40:06

       It's kinda cool. So, turns out though, that how well you groupitize predicts how well you do in maths.

   15. LFLex Fridman40:15

       Is, is it, uh, is it a raw talent or is just something that you can develop?

   16. JBJo Boaler40:19

       I don't think it's r- I don't think you're born groupitizing. I think that some kids have developed that, um, ability, if you like, and you can learn it. You can... so this to me is part of how wrong we have maths, that we think to tell whether a kid's good at maths, we're gonna give them a speed test on-

   17. LFLex Fridman40:38

       Right.

   18. JBJo Boaler40:39

       ... fact, on multiples. But actually, seeing how kids group dots could be a more important assessment of how well they're gonna do in maths. Anyway, I diverge. What, what I like to do though when I start off with kids is show them. "I'm gonna give you math problems. I'm gonna value the different ways you see them." And turns out you can do this kind of problem asking people how they group dots with young children or with graduate students, and it's engaging for all of them.

   19. LFLex Fridman41:09

       Is, um... you talk about creativity a little bit and flexibility i- in your book Limitless. Wh- what's the role of that? So, it sounds like there's a bit of that-

   20. JBJo Boaler41:18

       Mm-hmm.

   21. LFLex Fridman41:19

       ... kind of thing involved in groupitizing.

   22. JBJo Boaler41:22

       Yeah.

   23. LFLex Fridman41:23

       (laughs)

   24. JBJo Boaler41:23

       Yeah.

   25. LFLex Fridman41:24

       We- I love this term.

   26. JBJo Boaler41:25

       (laughs)

   27. LFLex Fridman41:25

       So what's, wh- what would you say is the role of creativity and flexibility-

   28. JBJo Boaler41:29

       I think-

   29. LFLex Fridman41:29

       ... in, in the learning of math?

   30. JBJo Boaler41:31

       ... I think what we know now is that what we need for this 21st century world we live in is a flexible mind. It's- school should not really be about teaching kids particular methods but teaching them to approach problems with flexibility. Being creative, thinking creatively is really important. So, people don't think the words maths (laughs) and creativity come together, but I... that's what I love about maths is the creative different ways you can see it. And so, helping our kids, there's a book I like a lot by... written by a physicist. You probably know this book called Elastic.
7. 56:35 – 1:00:55

   youcubed

   1. LFLex Fridman56:35

      You mentioned YouCubed, so what's the mission, what's the goal? You, you mentioned how it started, but what's, uh-

   2. JBJo Boaler56:42

      Mm-hmm.

   3. LFLex Fridman56:43

      ... um, yeah, w- where are you at now and what do you, what's your dream with it or what are the kind of things that people should go and check out on there?

   4. JBJo Boaler56:50

      Yeah. We started YouCubed, I guess it was about five years ago now, and we've had over 52 million visitors to the site, so I'm-

   5. LFLex Fridman56:57

      Wow.

   6. JBJo Boaler56:58

      ... very happy about that. And our goal is to share good ideas for teaching with teachers, students, parents in maths, and to help... We have a sort of sub-goal of erasing maths anxiety, that's important to us, but also to share maths as this beautiful, creative subject and, um, it's been really great. Uh, we have lessons on the site, but one of the thing, one of the reasons I thought this was needed is there's a lot of knowledge in the academy about how to teach maths well. Loads and loads of research and journals and lots of things written up, but teachers don't read it, they, they don't have access to it, they're often behind pay walls, they, they're written in really inaccessible ways so people wouldn't want to read them or understand them. So, this I see as a big problem, you have this whole industry of people finding out how to teach well, not sharing it with the people who are teaching. So, um, that's why we made YouCubed, and instead of just putting articles up saying, "Here's some things to read about how to teach well," we translated what was coming from research into things that teacher could use. So, lessons, there were videos to show kids and, um, there were tips for parents, there were all sorts of things on the site and it's been amazing as we ha- we took inspiration from the Week of Code, which-

   7. LFLex Fridman58:25

      Mm-hmm.

   8. JBJo Boaler58:26

      ... got teachers to focus on coding for a week and, um, we have this thing called the Week of Inspirational Maths.

   9. LFLex Fridman58:33

      (laughs)

   10. JBJo Boaler58:33

       And we say, "Just try it for a week, just, just give us one week and try it and see what happens." And so it's been downloaded millions of times, teachers use it every year, they start the school year with it and what they tell us is, "It was amazing, the kids' lights were on, they were excited, they loved it, and then the week finished and I opened my textbooks and the lights went out-"

   11. LFLex Fridman58:58

       (laughs)

   12. JBJo Boaler58:58

       "... and they were not interested."

   13. LFLex Fridman59:00

       Yeah. But, but getting that first inspiration is still powerful. I mean, even-

   14. JBJo Boaler59:04

       It is. I, I wish, I mean, my, what I would love is if we could actually extend that for the whole year.

   15. LFLex Fridman59:11

       Mm-hmm.

   16. JBJo Boaler59:11

       We're a small team at Stanford and we're trying to keep up with great things to put on the site, um, we haven't the capacity to produce these creative visual maths tasks for every year group for every day, but I would love to do that.

   17. LFLex Fridman59:27

       How difficult is it to do? I mean, it's, uh, to, to come up (sighs) with, uh, visual formulations of these, uh, big important topics you need to think about in a way that, you know, that, uh, that, that, that you could teach?

   18. JBJo Boaler59:43

       I mean, it, we can do it. We actually, we went from the Week of Inspirational Maths and we made K8 maths books with exactly that.

   19. LFLex Fridman59:52

       Nice.

   20. JBJo Boaler59:52

       Big ideas, rich activities, visuals. We just finished the last one, we've been doing it for five years and it's been exhausting, and we just finished. So now, there's a whole K8 set of books and they're organized in that way, "These are the big ideas, here are rich, deep activities."

   21. LFLex Fridman1:00:10

       Mm-hmm.

   22. JBJo Boaler1:00:10

       Um, they're not though what you can do every day for a year. They're... So some teachers use them as a kind of supplement to their boring textbook and some people have said, "Okay, this is the year, this book tells us what the year is and then we'll supplement these big activities with..."

   23. LFLex Fridman1:00:29

       Mm-hmm.

   24. JBJo Boaler1:00:30

       Um, so they're being used and teachers really like them and are really happy about them. I just always want more. And I, and I guess one of the things I would like for YouCubed, one of my personal goals is that every teacher of maths knows about YouCubed.

   25. LFLex Fridman1:00:44

       (laughs) yeah.

   26. JBJo Boaler1:00:45

       At the moment, um, a lot of teachers who come to us are really happy they found it, but there's a lot of other teachers who don't know that it exists.

   27. LFLex Fridman1:00:53

       Well, I hope this helps.

8. 1:00:55 – 1:21:29

   Best methods for studying math

   1. LFLex Fridman1:00:55

   2. JBJo Boaler1:00:55

      Yeah.

   3. LFLex Fridman1:00:56

      From a student perspective and not in the classroom but at home studying, you know, is there some, um, advice you can give on how to best study mathematics? So what's the role-

   4. JBJo Boaler1:01:10

      Hmm.

   5. LFLex Fridman1:01:10

      ... of the student outside the classroom?

   6. JBJo Boaler1:01:13

      Yeah. I think one thing we know is a lot of people when they review material, whether it's maths or anything else, don't do it in the best way.I think a problem a lot of people have is they read through maybe a teacher's explanation or a way of doing maths, and it makes sense, and they think, "Oh, yeah, I've got that," and they move on. Um, but then it's not until you come to try and work on something and do a problem that you actually realize you didn't really understand, it-

   7. LFLex Fridman1:01:42

      Mm-hmm.

   8. JBJo Boaler1:01:42

      ... just seemed to make sense. So, I would say, this is also something that neuroscientists talk about, to keep giving yourself questions is a really good way to study rather than looking through lots of material. It's almost like giving yourself lots of tests is a good way to actually deeply understand things and know what you do when you don't understand.

   9. LFLex Fridman1:02:07

      So, would the questions be in the form of the material you're reviewing is the answer to that question? Or is it almost like beyond, it's the polygon thing you mentioned-

   10. JBJo Boaler1:02:17

       Mm-hmm. Mm-hmm.

   11. LFLex Fridman1:02:18

       ... from a square? Is it almost like, "I wonder what is the bigger picture?" Always kind of asking-

   12. JBJo Boaler1:02:24

       Mm-hmm.

   13. LFLex Fridman1:02:24

       ... of like, how is this extended and so on?

   14. JBJo Boaler1:02:26

       Yeah. That, that, that would be great. And it's a similar... I mean, a question I get asked a lot is about homework, what is a good thing for kids to do for homework? And one of the recommendations I give is to not have kids just do lots of questions for homework, but to actually ask them to reflect on what they've learned, like, "What was the big idea you were work- you learned today?" Or, "What did you find difficult? What did you struggle with? What was something that was exciting?" Um, then kids go home and they have to kind of reflect in a deeper way. A lot of times, I don't know if you had this experience as a math student, lots of people do, kids are going through maths questions, they're successful, they get them right, but they don't even really know what they're about.

   15. LFLex Fridman1:03:13

       Mm-hmm.

   16. JBJo Boaler1:03:13

       They... And a lot of kids go through many years of maths like that, doing lots of questions, but not really knowing what even the topic is or what it's about, what it's important for. So, having students go back and think at the end of a day, "What was the big idea from this maths lesson? Why is it important? Where would I find that in real life?" Those are really good questions for kids to be thinking about.

   17. LFLex Fridman1:03:39

       It's probably for everybody to be thinking about. I think-

   18. JBJo Boaler1:03:42

       Yeah.

   19. LFLex Fridman1:03:42

       ... most of us go through life never asking, like, the bigger question.

   20. JBJo Boaler1:03:48

       Mm-hmm.

   21. LFLex Fridman1:03:48

       Always like, you know, those like layers of why questions that kids ask when they're very young?

   22. JBJo Boaler1:03:53

       Yeah.

   23. LFLex Fridman1:03:54

       We, we need to keep doing that.

   24. JBJo Boaler1:03:56

       We do.

   25. LFLex Fridman1:03:56

       You know? Like what, uh, that's the, you know, whatever the term is you call first principles thinking, some people call it that.

   26. JBJo Boaler1:04:02

       Mm-hmm.

   27. LFLex Fridman1:04:03

       Which is like, "Why are we doing it this way?" So, one, one nice thing is to do that 'cause there's usually a good answer. Like, "The reason we did it this way is because it works for this reason." But then if you want to do something totally novel, is you'll say, "Well, we've been doing it this way, um, because of historical reasons, but really this is not the best way to do it, there might be other ways." And, and that's how invention happens.

   28. JBJo Boaler1:04:34

       Right.

   29. LFLex Fridman1:04:34

       And then you get... You know, that's really useful in every aspect of life, like choosing your career, choosing your, um, I don't know, w- where you live-

   30. JBJo Boaler1:04:44

       Yeah.
9. 1:21:29 – 1:24:59

   Advice for young people

   1. JBJo Boaler1:21:29

   2. LFLex Fridman1:21:30

      Do you have advice for young people... We've been talking about mathematics quite a bit but, uh, in terms of their journey through education, through their career choices, through life, maybe middle school, high school, undergrad students, on how to live a life they're, they can be proud of?

   3. JBJo Boaler1:21:50

      I think if I were to give advice to people, especially young people, my advice would be to always, it sounds really corny, but always believe in yourself and know that you can achieve because although that sounds like obvious, of course we want kids to know that they can achieve things, I know that millions of kids who are in the school system have been given the message they cannot do things.

   4. LFLex Fridman1:22:17

      (laughs)

   5. JBJo Boaler1:22:17

      And adults too. They have the idea, "Oh, I did okay in this. I went into this job because those other things I could never have done okay in."

   6. LFLex Fridman1:22:26

      Mm-hmm.

   7. JBJo Boaler1:22:27

      So actually when they hear, "Hey, maybe you could do those other things," even adults think, "You know, (laughs) maybe I can." And they go back and they encounter this knowledge and they relearn things and they change careers and amazing things happen so for me I think that message is really important. You can learn anything. Scientists try and find a limit. They're always trying to find a limit like how much can you really learn? What's the limit to how much you can learn? And they always come away not being able to find it. People can just go further and further and further and that is true of people born with brain, um, you know, areas of their brain that aren't functioning well, that have what we call special needs. Some of those people also go on to develop and do amazing things. So I think that really experiencing that, knowing that, feeling, not just saying it but knowing it-

   8. LFLex Fridman1:23:20

      Mm-hmm.

   9. JBJo Boaler1:23:21

      ... deeply you can learn anything is, um, um, something I wish all people would have.

   10. LFLex Fridman1:23:28

       Actually also applies when you've achieved some level of success too. What I find like in my life with people that love me, when you achieve success, they, they keep celebrating your success and they want you to keep doing the thing that you were successful at as opposed to s- believing in that you can do-

   11. JBJo Boaler1:23:48

       Something else.

   12. LFLex Fridman1:23:49

       ... the, the, something else.

   13. JBJo Boaler1:23:49

       Mm-hmm.

   14. LFLex Fridman1:23:49

       Something big. Whatever your heart says to do.

   15. JBJo Boaler1:23:51

       Right.

   16. LFLex Fridman1:23:51

       And one of the things that I realized the value of this, um, you know, quite recently which is sad to say, is how important it is to seek out, uh, when you're younger, to seek out mentors.

   17. JBJo Boaler1:24:05

       Mm-hmm.

   18. LFLex Fridman1:24:05

       To seek out the people, like surround yourself with people that will believe in you.

   19. JBJo Boaler1:24:10

       Yeah.

   20. LFLex Fridman1:24:10

       It's like a little bit is-

   21. JBJo Boaler1:24:12

       Yeah.

   22. LFLex Fridman1:24:12

       ... is on you.

   23. JBJo Boaler1:24:13

       Mm-hmm.

   24. LFLex Fridman1:24:13

       (laughs) It's like, uh, you don't get that, um... Sometimes if you go to like grad school y- you think you kind of land on a mentor, maybe you pick a mentor based on the topic they're interested in but the reality is the people you surround yourself with, they're going to define your life-

   25. JBJo Boaler1:24:31

       Yeah.

   26. LFLex Fridman1:24:31

       ... trajectory. So select-

   27. JBJo Boaler1:24:34

       That's really true.

   28. LFLex Fridman1:24:34

       ... people that-

   29. JBJo Boaler1:24:34

       That's really true. And get away-

   30. LFLex Fridman1:24:36

       ... believe in you.

Episode duration: 1:30:40